Permutation and Combination: Test 1

10 questions · 15 minutes · scoring and calculator rules shown before you begin

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Permutation and Combination Test 1: questions and answers

Take the test first if you want an honest score. The answers and solutions below are folded away until you open them.

  1. 1. In how many different ways can the letters of the word 'MOTHER' be arranged?
    1. 360
    2. 36
    3. 120
    4. 720

    Reference: q-ff9de5e3-77 · Report this question

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    Answer: D. 720

    The word has 6 different letters, so the number of arrangements is 6! = 720.
  2. 2. In how many different ways can the letters of the word 'BALLOON' be arranged?
    1. 630
    2. 1,260
    3. 2,520
    4. 5,040

    Reference: q-c85b5e7d-78 · Report this question

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    Answer: B. 1,260

    There are 7 letters with L repeated 2 times and O repeated 2 times. Arrangements = 7! / (2! × 2!) = 1,260.
  3. 3. In how many ways can a committee of 3 members be selected from 7 persons?
    1. 210
    2. 21
    3. 35
    4. 27

    Reference: q-e3789f30-74 · Report this question

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    Answer: C. 35

    Number of ways = 7C3 = 35.
  4. 4. In how many ways can a committee of 3 men and 1 woman be formed from 4 men and 4 women?
    1. 70
    2. 10
    3. 8
    4. 16

    Reference: q-9e94ca35-88 · Report this question

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    Answer: D. 16

    Men can be chosen in 4C3 = 4 ways and women in 4C1 = 4 ways. Total = 4 × 4 = 16.
  5. 5. 17 people attend a meeting and each shakes hands with every other person exactly once. How many handshakes take place?
    1. 139
    2. 136
    3. 289
    4. 272

    Reference: q-2bc73874-119 · Report this question

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    Answer: B. 136

    Number of handshakes = 17C2 = 17 × 16 / 2 = 136.
  6. 6. In how many different ways can the letters of the word 'BLACK' be arranged?
    1. 25
    2. 24
    3. 120
    4. 60

    Reference: q-2d7ab0e9-76 · Report this question

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    Answer: C. 120

    The word has 5 different letters, so the number of arrangements is 5! = 120.
  7. 7. In how many different ways can the letters of the word 'COFFEE' be arranged?
    1. 360
    2. 90
    3. 720
    4. 180

    Reference: q-6a45b18-77 · Report this question

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    Answer: D. 180

    There are 6 letters with F repeated 2 times and E repeated 2 times. Arrangements = 6! / (2! × 2!) = 180.
  8. 8. In how many ways can a committee of 3 members be selected from 6 persons?
    1. 16
    2. 18
    3. 120
    4. 20

    Reference: q-d9ae4471-74 · Report this question

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    Answer: D. 20

    Number of ways = 6C3 = 20.
  9. 9. In how many ways can a committee of 3 men and 2 women be formed from 7 men and 6 women?
    1. 525
    2. 1,287
    3. 684
    4. 50

    Reference: q-39cf24bd-88 · Report this question

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    Answer: A. 525

    Men can be chosen in 7C3 = 35 ways and women in 6C2 = 15 ways. Total = 35 × 15 = 525.
  10. 10. 15 people attend a meeting and each shakes hands with every other person exactly once. How many handshakes take place?
    1. 105
    2. 225
    3. 210
    4. 107

    Reference: q-67f46b46-119 · Report this question

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    Answer: A. 105

    Number of handshakes = 15C2 = 15 × 14 / 2 = 105.

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